Fit by assuming every observation is an equilibrium
“Their use [equilibrium assumptions] in the past undoubtedly contributed to a number of major fishery collapses.” Haddon (2011)
Where Social Science goes to die - part 2
The profit maximizing boat; decides:
Where to fish
Optimal path
Number of trips per season
State space is immense:
Belief state of biomass available per fishing spot, per species, per time step
Location and action of all competitors
Bellman equation unsolvable
Metaphysical Dualism
What does computational tractability tells us about the real world?
“If your laptop can’t find it, then neither can the market.”
Pool player analogy
Church-Turing thesis
Two solutions in fisheries economics
Ignore dynamics
Discrete choice models
Add indicators to correct for dynamics
“this is akin to postponing opening a gift in the knowledge that the joy of consumption will be greater for the wait” Baerenklau (2005)
Two solutions in fisheries economics
Ignore fisheries:
Assume no space
Assume perfect knowledge
Assume fishing doesn’t kill of fish
Assume one boat
Pragmatism
Logbook data
Surveys
“I have only 5 spots and cycle through them”
“If in a bind, track highliner on radar and copy them”
“Explore a fixed proportion of tows”
“Draw peaks and valleys on maps”
Flexibility and Lucas critique
Zoo approach
Collect decision algorithms
From interviews
From CS-literature
Implement them in the same agent-based model
Test strengths/weaknesses in theory
Compare to real data
Use it for policy suggestions and sensitivity analysis
The One Agent Problem
The One Agent Problem
Find the most profitable spot to fish
Constraints:
No biomass information
No model knowledge
Environment changes over time
Subproblems:
How to explore
Explore-Exploit Tradeoff
Explore or Exploit ?
Explore or Exploit ?
Explore-Exploit
Stochastically choose to explore next trip with probability \(p\)
Explore in the neighborhood of where you currently go
One Agent world
One Agent sample run
Scaling issues
Scaling issues
Scaling issues
L’enfer, c’est les autres
Other boats consume biomass
You can use other boats information
How to imitate?
With probability \(p\) explore, otherwise copy somebody who’s doing better
Explore-Exploit-Imitate
\begin{algorithm}
\caption{Explore-Exploit-Imitate}
\begin{algorithmic}
\WHILE{game is not over}
\IF{$\text{random} < \epsilon$}
\COMMENT{with probability $\epsilon$, explore}
\STATE $\hat \delta \sim U[-\delta,\delta]$
\STATE $\text{position} \leftarrow \text{position} + \hat \delta$
\COMMENT{explore by shocking your position by $\delta$}
\ELSE
\STATE $\text{profits}_f$ are the profits made by your most profitable friend
\STATE $\text{profits}_{\text{me}}$ are the profits just made by this agent
\IF{$\text{profits}_f>\text{profits}_{\text{me}}$}
\STATE copy friend location
\ELSE
\STATE stay at current location
\ENDIF
\ENDIF
\ENDWHILE
\end{algorithmic}
\end{algorithm}
Two Agents sample run
Many Agents
Cui prodest?
Model free
Adaptive
Oil Prices
Fish the Line (part 1)
Fish the Line (part 2)
Optimization
Gravitational Search
\begin{algorithm}
\caption{Gravitational Search implementation}
\begin{algorithmic}
\STATE $\text{velocity} \leftarrow \text{velocity}_0$
\WHILE{game is not over}
\FOR{$\text{player}=0$ to $N$}
\COMMENT{turn all other players' rewards into masses}
\STATE $\text{mass[player]}\leftarrow \frac{\text{profits[player]}-\min(\text{profits})}{\max(\text{profits})-\min(\text{profits})}$
\COMMENT{peek at everyone's profits and normalize them}
\ENDFOR
\STATE select the top $Z$ masses
\STATE $\text{acceleration} \leftarrow 0$
\FORALL{$i$ such that $\text{masses[i]}$ is one of the top $Z$ masses}
\STATE $\text{acceleration} \leftarrow \text{acceleration} + G * \frac{\text{masses[here]}*\text{masses[i]}} {\text{distance(here,i))}}$
\COMMENT{selective gravitational pull}
\ENDFOR
\STATE $\epsilon \sim U[0,1]$
\COMMENT{Draw random inertia}
\STATE $\text{velocity} \leftarrow \epsilon \cdot\text{velocity} + \text{accelleration}$
\STATE $\text{position} = \text{position} + \text{velocity}$
\STATE play position
\ENDWHILE
\end{algorithmic}
\end{algorithm}
Gravitational Search - Demo
Kernel Regression
Kernel Regression - Demo
Which algorithm performs best in which scenarios?
Which algorithm performs best in which scenarios -pt 2
Which algorithm performs best in real scenarios
Estimating Models!
Complicated model depends on parameter vector \(\theta\)
All model estimation strategies do:
Pick some summaries of data \(X\)\[ S = S_1(X), \dots, S_n(X) \]
Generate similar summaries from model: \[ \hat S(\theta) = S_1(\theta),\dots, S_n(\theta) \]
Minimize weighted distance: \[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]
In economics one often assumes:
Ergodicity
1 to 1 mapping
\(\Rightarrow\) consistency!
Issues
\[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]
How to minimize?
ABC
BACCO (GP)
Simulated Annealing
Which summary statistics?
4 to 1? (Altonji,Smith and Vidangos 2013)
Computational Costs? Collinearities?
Which weight?
In theory \(W \to \Omega^{-1}\)
In practice that is almost never better
Solution?
\[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]
Just a complicated mapping \(S \to \theta\)
Discover it directly by regression
Run the model many times, for different \(\hat \theta\), generate \(\hat S(\theta)\)